APAndrew Miller hopes to finally unlock the potential that made him a top-10 draft pick.

PORT SAINT LUCIE, Fla. – It was the day of the left-handed reliever for the Boston Red Sox as they made the three-hour trek across Alligator Alley to face the New York Mets Sunday.

Boston fell 6-5 at Digital Domain Park on an eighth-inning home run by New York outfielder Lucas Duda, but the game served a greater purpose in pitting left-handed bullpen candidates Rich Hill, Andrew Miller and Hideki Okajima against one another.

“I didn’t even notice that until (Okajima) went in,” Hill said.

The incumbent Okajima pitched one scoreless inning, as he continues to rebound after surrendering five hits and four runs against Minnesota Feb. 27.

But more interesting was the juxtaposition between Miller and Hill, both of whom were picked up off the scrap heap in low-risk, high-reward moves over the last year and are looking to displace Okajima, who posted a 4.50 ERA in 2010.

Hill gave up one hit and struck out one over two scoreless innings, while Miller had a bipolar performance, giving up three runs in his first inning before retiring the side in order in his second.

“In (Miller’s) first inning he didn’t locate very well and he paid the price for it,” Francona said. “He got stretched out a little bit and threw a few good breaking balls. There’s a lot to work with there.”

At least one of those players will not break camp with Boston. Typically a team only carries one lefty specialist, but Francona is open to the possibility of carrying two if it makes baseball sense.

Hill, who made six appearances with Boston last season, is trying to win a spot in the Red Sox bullpen after injuries and ineffectiveness plagued him the previous three seasons.

Hill retired the first batter he faced, gave up a weak single and then sat down the next five in order.

“I think I was aggressive,” Hill said. “I threw everything with conviction and stayed aggressive and pitched to my strengths.”

Hill, 30, a former overhand pitcher, is now throwing side-armed at the behest of former Red Sox pitching coach John Farrell, now the manager of the Toronto Blue Jays.

He has now thrown four innings from the slot this spring and has yet to allow a run.

But even though he’s been effective, Francona isn’t convinced with Hill’s new throwing motion.

“There were a few breaking balls from over the top that he didn’t command,” Francona said. “Consistency is going to be a big thing with Rich.”

Miller, who was acquired in a November trade that sent Justin Richardson to the Marlins, has the most upside of the bunch.

Once considered the best pitching prospect in baseball and the centerpiece of the deal that landed Miguel Cabrera in Detroit from Florida, Miller, like Hill, failed as a starter and is trying to fight his way back to the majors through a bullpen spot.

Sunday’s bad inning aside, Miller has had Boston’s camp buzzing so far with his performance.

In his first two appearances, he combined for three strikeouts and no walks over two innings, and touched 99 on the radar gun.

“(Those were) two of the funnest innings in spring,” Francona told the assembled media prior to the game. “There’s not much not to like.”

No one would proclaim a winner of lefty-mania, though Hill did allow a little bit of insight into where he feels he stands.

“I think if I keep pitching the way I have and control what I can control,” Hill said, “the rest should take care of itself.”